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updating standard preamble formula names
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,27 +1,27 @@ | ||
| tff(type, type, general: $tType). | ||
| tff(type, type, symbol: $tType). | ||
| tff(type, type, f__integer__: ($int) > general). | ||
| tff(type, type, f__symbolic__: (symbol) > general). | ||
| tff(type, type, c__infimum__: general). | ||
| tff(type, type, c__supremum__: general). | ||
| tff(type, type, p__is_integer__: (general) > $o). | ||
| tff(type, type, p__is_symbolic__: (general) > $o). | ||
| tff(type, type, p__less_equal__: (general * general) > $o). | ||
| tff(type, type, p__less__: (general * general) > $o). | ||
| tff(type, type, p__greater_equal__: (general * general) > $o). | ||
| tff(type, type, p__greater__: (general * general) > $o). | ||
| tff(axiom, axiom, ![X: general]: (p__is_integer__(X) <=> (?[N: $int]: (X = f__integer__(N))))). | ||
| tff(axiom, axiom, ![X1: general]: (p__is_symbolic__(X1) <=> (?[X2: symbol]: (X1 = f__symbolic__(X2))))). | ||
| tff(axiom, axiom, ![X: general]: ((X = c__infimum__) | p__is_integer__(X) | p__is_symbolic__(X) | (X = c__supremum__))). | ||
| tff(axiom, axiom, ![N1: $int, N2: $int]: ((f__integer__(N1) = f__integer__(N2)) <=> (N1 = N2))). | ||
| tff(axiom, axiom, ![S1: symbol, S2: symbol]: ((f__symbolic__(S1) = f__symbolic__(S2)) <=> (S1 = S2))). | ||
| tff(axiom, axiom, ![N1: $int, N2: $int]: (p__less_equal__(f__integer__(N1), f__integer__(N2)) <=> $lesseq(N1, N2))). | ||
| tff(axiom, axiom, ![X1: general, X2: general]: ((p__less_equal__(X1, X2) & p__less_equal__(X2, X1)) => (X1 = X2))). | ||
| tff(axiom, axiom, ![X1: general, X2: general, X3: general]: ((p__less_equal__(X1, X2) & p__less_equal__(X2, X3)) => p__less_equal__(X1, X3))). | ||
| tff(axiom, axiom, ![X1: general, X2: general]: (p__less_equal__(X1, X2) | p__less_equal__(X2, X1))). | ||
| tff(axiom, axiom, ![X1: general, X2: general]: (p__less__(X1, X2) <=> (p__less_equal__(X1, X2) & (X1 != X2)))). | ||
| tff(axiom, axiom, ![X1: general, X2: general]: (p__greater_equal__(X1, X2) <=> p__less_equal__(X2, X1))). | ||
| tff(axiom, axiom, ![X1: general, X2: general]: (p__greater__(X1, X2) <=> (p__less_equal__(X2, X1) & (X1 != X2)))). | ||
| tff(axiom, axiom, ![N: $int]: p__less__(c__infimum__, f__integer__(N))). | ||
| tff(axiom, axiom, ![N: $int, S: symbol]: p__less__(f__integer__(N), f__symbolic__(S))). | ||
| tff(axiom, axiom, ![S: symbol]: p__less__(f__symbolic__(S), c__supremum__)). | ||
| tff(general_type, type, general: $tType). | ||
| tff(symbol_type, type, symbol: $tType). | ||
| tff(f__integer___decl, type, f__integer__: ($int) > general). | ||
| tff(f__symbolic___decl, type, f__symbolic__: (symbol) > general). | ||
| tff(inf_type, type, c__infimum__: general). | ||
| tff(sup_type, type, c__supremum__: general). | ||
| tff(p__is_integer__decl, type, p__is_integer__: (general) > $o). | ||
| tff(p__is_symbolic__decl, type, p__is_symbolic__: (general) > $o). | ||
| tff(p__less_equal__decl, type, p__less_equal__: (general * general) > $o). | ||
| tff(p__less__decl, type, p__less__: (general * general) > $o). | ||
| tff(p__greater_equal__decl, type, p__greater_equal__: (general * general) > $o). | ||
| tff(p__greater__decl, type, p__greater__: (general * general) > $o). | ||
| tff(p__is_integer__def_ax, axiom, ![X: general]: (p__is_integer__(X) <=> (?[N: $int]: (X = f__integer__(N))))). | ||
| tff(p__is_symbolic__def_ax, axiom, ![X1: general]: (p__is_symbolic__(X1) <=> (?[X2: symbol]: (X1 = f__symbolic__(X2))))). | ||
| tff(general_universe_ax, axiom, ![X: general]: ((X = c__infimum__) | p__is_integer__(X) | p__is_symbolic__(X) | (X = c__supremum__))). | ||
| tff(f__integer__def_ax, axiom, ![N1: $int, N2: $int]: ((f__integer__(N1) = f__integer__(N2)) <=> (N1 = N2))). | ||
| tff(f__symbolic__def_ax, axiom, ![S1: symbol, S2: symbol]: ((f__symbolic__(S1) = f__symbolic__(S2)) <=> (S1 = S2))). | ||
| tff(numeral_ordering_ax, axiom, ![N1: $int, N2: $int]: (p__less_equal__(f__integer__(N1), f__integer__(N2)) <=> $lesseq(N1, N2))). | ||
| tff(antisymmetric_ordering_ax, axiom, ![X1: general, X2: general]: ((p__less_equal__(X1, X2) & p__less_equal__(X2, X1)) => (X1 = X2))). | ||
| tff(transitive_ordering_ax, axiom, ![X1: general, X2: general, X3: general]: ((p__less_equal__(X1, X2) & p__less_equal__(X2, X3)) => p__less_equal__(X1, X3))). | ||
| tff(strongly_connected_ordering_ax, axiom, ![X1: general, X2: general]: (p__less_equal__(X1, X2) | p__less_equal__(X2, X1))). | ||
| tff(p__less__def_ax, axiom, ![X1: general, X2: general]: (p__less__(X1, X2) <=> (p__less_equal__(X1, X2) & (X1 != X2)))). | ||
| tff(p__greater_equal__def_ax, axiom, ![X1: general, X2: general]: (p__greater_equal__(X1, X2) <=> p__less_equal__(X2, X1))). | ||
| tff(p__greater__def_ax, axiom, ![X1: general, X2: general]: (p__greater__(X1, X2) <=> (p__less_equal__(X2, X1) & (X1 != X2)))). | ||
| tff(minimal_element_ax, axiom, ![N: $int]: p__less__(c__infimum__, f__integer__(N))). | ||
| tff(numerals_less_than_symbols_ax, axiom, ![N: $int, S: symbol]: p__less__(f__integer__(N), f__symbolic__(S))). | ||
| tff(maximal_element_ax, axiom, ![S: symbol]: p__less__(f__symbolic__(S), c__supremum__)). |