Nuprl Lemma : cosine_functionality
∀[x,y:ℝ]. cosine(x) = cosine(y) supposing x = y
Proof
Definitions occuring in Statement :
cosine: cosine(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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
and: P ∧ Q,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
nequal: a ≠ b ∈ T ,
int_nzero: ℤ-o,
top: Top
Latex:
\mforall{}[x,y:\mBbbR{}]. cosine(x) = cosine(y) supposing x = y
Date html generated:
2020_05_20-AM-11_26_00
Last ObjectModification:
2020_01_06-PM-00_20_39
Theory : reals
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