Nuprl Lemma : int_term_value_functionality
∀[f:ℤ ⟶ ℤ]. ∀[t1,t2:int_term()]. int_term_value(f;t1) = int_term_value(f;t2) ∈ ℤ supposing t1 ≡ t2
Proof
Definitions occuring in Statement :
equiv_int_terms: t1 ≡ t2,
int_term_value: int_term_value(f;t),
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
guard: {T},
equiv_int_terms: t1 ≡ t2,
all: ∀x:A. B[x]
Lemmas referenced :
equiv_int_terms_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mforall{}[f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}]. \mforall{}[t1,t2:int\_term()]. int\_term\_value(f;t1) = int\_term\_value(f;t2) supposing t1 \mequiv{} t2
Date html generated:
2016_05_14-AM-06_59_54
Last ObjectModification:
2015_12_26-PM-01_12_35
Theory : omega
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