Nuprl Lemma : sinh_functionality
∀[x,y:ℝ]. sinh(x) = sinh(y) supposing x = y
Proof
Definitions occuring in Statement :
sinh: sinh(x),
req: x = y,
real: ℝ,
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,
sinh: sinh(x),
implies: P ⇒ Q,
prop: ℙ,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
sinh_wf,
req_wf,
real_wf,
int-rdiv_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
nequal_wf,
rsub_wf,
expr_wf,
rexp_wf,
rminus_wf,
req_weakening,
req_functionality,
int-rdiv_functionality,
rsub_functionality,
expr-req,
rexp_functionality,
rminus_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
natural_numberEquality,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
voidElimination,
baseClosed,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. sinh(x) = sinh(y) supposing x = y
Date html generated:
2017_10_04-PM-10_40_27
Last ObjectModification:
2017_06_21-PM-01_00_48
Theory : reals_2
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