Nuprl Lemma : itermSubtract_functionality
∀[a,b,c,d:int_term()]. (a "-" c ≡ b "-" d) supposing (a ≡ b and c ≡ d)
Proof
Definitions occuring in Statement :
equiv_int_terms: t1 ≡ t2,
itermSubtract: left "-" right,
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
equiv_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
int_term_value: int_term_value(f;t),
itermSubtract: left "-" right,
int_term_ind: int_term_ind,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
subtract_wf,
int_term_value_wf,
equiv_int_terms_wf,
int_term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
promote_hyp,
instantiate,
lemma_by_obid,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
functionEquality,
lambdaEquality,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a,b,c,d:int\_term()]. (a "-" c \mequiv{} b "-" d) supposing (a \mequiv{} b and c \mequiv{} d)
Date html generated:
2016_05_14-AM-06_59_59
Last ObjectModification:
2015_12_26-PM-01_12_37
Theory : omega
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