Nuprl Lemma : itermSubtract_functionality_wrt_req
∀[a,b,c,d:int_term()]. (a (-) c ≡ b (-) d) supposing (a ≡ b and c ≡ d)
Proof
Definitions occuring in Statement :
req_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,
req_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
real_term_value: real_term_value(f;t),
itermSubtract: left (-) right,
int_term_ind: int_term_ind,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
real_wf,
req_witness,
real_term_value_wf,
itermSubtract_wf,
req_int_terms_wf,
int_term_wf,
rsub_wf,
req_weakening,
req_functionality,
rsub_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
functionEquality,
intEquality,
extract_by_obid,
lambdaEquality,
isectElimination,
functionExtensionality,
applyEquality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[a,b,c,d:int\_term()]. (a (-) c \mequiv{} b (-) d) supposing (a \mequiv{} b and c \mequiv{} d)
Date html generated:
2017_10_02-PM-07_18_45
Last ObjectModification:
2017_04_02-PM-11_37_09
Theory : reals
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